Resistance thermometers known in the art have a measuring structure made of platinum, which is arranged on a substrate. The measuring structure is in turn covered by a cover layer. The cover layer and the measuring structure in known resistance thermometers have different thermal coefficients of expansion. When known resistance thermometers are stressed by abrupt changes in temperature, alterations and damage, which act on the entire measuring structure and falsify the measurement values as a result, can occur at the boundary layer between the cover layer and the measuring structure. Consequently, a temperature measurement made by the resistance thermometer becomes more unreliable over time.